# Question about FMCW range-velocity plot

I am working on plotting range-velocity heatmap of the receiving FMCW signal. I actually have already plotted. However, I do not really understand the mapping relationship between Doppler FFT bin and velocity. I learned to map from 1d FFT bin to range with the following codes as the x-axis.

x = (0:ADCsample-1) - ADCsample/2;
% freq to dist;
x = x*3e8/2/slope;


Some notes, I plot the 2D FFT with nFFT = No of chirp in one frame =64.

Firstly, because the speed can be positive and negative (meaning approaching to and going from sensor if target is moving), you need to shift your doppler indices from [0, N-1] to [-N/2,N/2 - 1] by simple subtraction by N. Then you just multiply scale [-N/2,N/2-1] by:

lambda/(2*N*T_rpi)


where:
- lambda is wavelength for your FMCW radar (lambda = c/Fc, c - speed of light and Fc central transmit frequency of chirp - for 77-81GHz you would use 79GHz)
- N is number of chirps transmitted
- T_rpi is chirp repetion interval (meaning T_active + T_idle if you have idle time after chirp transmission)

If you use multiple transmitters in time division multiplexed mode, you would need to multiple by:

lambda/(2*N*T_rpi*n_tx)


You then gain scale in m/s.